A transitive group of degree \(pq\)  falls into one of the following
three classes: it either has blocks of size \(p\)  or it has blocks
of size \(q\)  or it is a primitive group. (For a detailed description
of these groups see [1]}, [2]}, [3]}, [4]}.)
In the latter case the group is either doubly transitive in which
case the intersection density is known to be equal to 1
(see [5]}) or it is simply primitive.
Using the fact that \(\rho (G)\le \rho (H)\)  for transitive groups
\(H\le G\)  (see [5]})
the list of all simply primitive groups is further
reduced to a shorter list of simply primitive groups containing
no imprimitive subgroups (see [7]}, [2]}).
For each group on this list the corresponding
intersection density will have
to be computed.
Coming back to imprimitive groups, the first of the above three
classes is the easiest to deal with
when considering intersection density. The following holds.
